Virginia copper leaf or Three seeded mercury. http://extension.missouri.edu/p/MP903-53
There isn’t much lawn or ornamental research data on Copper leaf control. In personal observations spring preEmergents have been helpful but not entirely successful in eliminating copperleaf. Adequate mulch and handpulling will be needed. Post emergents can be used in open areas. If left unchecked your invasive suspecions are correct.

It’s pretty, but I’d pull it.
(Acalypha rhomboidea) rhombic copperleaf
While I’m having difficulties finding online images in that colour, I find specimens in the garden after they’ve turned that colour.